Analysis of nucleon electromagnetic form factors from light-front holographic QCD: The spacelike region

We present a comprehensive analysis of the spacelike nucleon electromagnetic form factors and their flavor decomposition within the framework of light-front (LF) holographic QCD (LFHQCD) We show that the inclusion of the higher Fock components $|qqqq\overline{q}⟩$ has a significant effect on the spin-flip elastic Pauli form factor and almost zero effect on the spin-conserving Dirac form factor. We present light-front holographic QCD results for the proton and neutron form factors at any momentum transfer range, including asymptotic predictions, and show that our results agree with the available experimental data with high accuracy. In order to correctly describe the Pauli form factor we need an admixture of a five quark state of about 30% in the proton and about 40% in the neutron. We also extract the nucleon charge and magnetic radii and perform a flavor decomposition of the nucleon electromagnetic form factors. The free parameters needed to describe the experimental nucleon form factors are very few: two parameters for the probabilities of higher Fock states for the spin-flip form factor and a phenomenological parameter $r$, required to account for possible SU(6) spin-flavor symmetry breaking effects in the neutron, whereas the Pauli form factors are normalized to the experimental values of the anomalous magnetic moments. The covariant spin structure for the Dirac and Pauli nucleon form factors prescribed by ${\mathrm{AdS}}_5$ semiclassical gravity incorporates the correct twist scaling behavior from hard scattering and also leads to vector dominance at low energy.

Figure 1

Polarization measurements and predictions for the proton and neutron Dirac form factors [71, 72]. The blue line is the prediction of the proton Dirac FF from LFHQCD, Eq. (21) multiplied by $Q^4$. The orange and the green lines are predictions for the neutron Dirac FF, $Q^4{F}_1^n(Q^2)$, from Eq. (23) and from Eq. (26) with the phenomenological factor $r=2.08$, respectively. The dotted lines are the asymptotic predictions. The asymptotic value of the neutron FF is determined using $r=2.08$.

Figure 2

Polarization measurements and predictions for the proton and neutron Pauli form factors [71, 72]. The blue line is the proton Pauli FF, $Q^6{F}_2^p(Q^2)$ prediction, with ${\gamma }_p=0.27$ in Eq. (22). The green line is the prediction for the neutron Pauli FF, $Q^6{F}_2^n(Q^2)$, with ${\gamma }_n=0.38$ in Eq. (24) from LFHQCD. The dotted lines are the asymptotic predictions.

Figure 3

LFHQCD prediction and comparison with selected world data of the ratio $R_p={\mu }_p{G}_E^p/G_M^p$ from unpolarized cross section measurements from [12, 15, 16, 75] and polarization measurements from [7, 8, 76, 77, 78, 79, 80]. The LFHQCD prediction (blue line) from Eqs. (21) and (22) corresponds to the range $0\le Q^2\le 30{\mathrm{GeV}}^2$. The band represents an estimated theoretical uncertainty of the model. Our theoretical results agree well with the polarization data and are incompatible with the experimental results obtained from Rosenbluth separation. The dotted line is the asymptotic prediction $R_p(\infty )=-0.309$ with an estimated uncertainty of $\pm 0.12$.

Figure 4

Comparison of the neutron electric FF $G_E^n(Q^2)$ world data [84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94] with the LFHQCD prediction from Eqs. (23), (24) and (26).

Figure 5

Selected world data of the ratio $R_n={\mu }_n{G}_E^n/G_M^n$ from double polarization experiments, recoil polarization with deuterium target, asymmetry with polarized deuterium target, and asymmetry with polarized ${}^3\mathrm{He}$ target. The data points are taken from Refs. [71, 84, 85, 87, 91, 95, 96, 97]. For more data points and other theoretical predictions, see Ref. [5]. The dotted line is the asymptotic prediction $R_n(\infty )=0.864$ with an estimated uncertainty of $\pm 0.11$ for $r=2.08$ in Eq. (26).

Figure 6

LFHQCD prediction of the up and the down-quark contributions to the Dirac FF multiplied by $Q^4$. The data are from Ref. [72].

Figure 7

LFHQCD prediction of the up and the down-quark contributions to the Pauli FF multiplied by ${\chi }_q^{-1}{Q}^6$. The data are from Ref. [72].